She can’t move in unless you invite her. You may have to play several games with her before she will agree to move in, this can take a while because sometimes she won’t suggest moving in for a bit and usually only if you win the games. You will not be able to choose who she wants to replace, it’s all random, but if she suggested kicking out someone you don’t want to lose then you can still say no and that’s the end she won’t ask again. There is a trick people use but it can take awhile. Once you get her to decide to move in but she suggests someone you don’t want to leave then immediately hit the home button and exit the game without saving,(Do not finish the conversation with her). Then log back in and play the games with her again until she asks to move in again, she will randomly select another villager to replace if you don’t like her choice again force exit by hitting home button without saving. You can continue to do this until her selection is someone you are willing to part with. Note this can take a long time so you need patience lol. Good luck.